And it seems like it would take a massive amount of ground work to be able to interpret correctly, if the findings aren't a proxy for neuroinflammation. Which seems more and more likely. If there is something here, my sense is that we'll make sense of it by working backwards once the mechanism of ME/CFS is already known, rather than being lead to the mechanism by these findings.
Technically I'm supposed to be good at math, they gave me a PhD. This is the first time in years I've been unfoggy enough to think about it though, so apologies for ramblingI'm not that good at math but I think the very free water (with diffusion > 2.5 μm2/ms) doesn't even enter their equation.
The second part represents the isotropic components, an integral from a to b where "a and b are the low and high diffusivity limits for the isotropic diffusion spectrum f(D)." Given the further explanation in the text, one is tempted to assume that a = 0.3 and b = 2.5 μm2/ms. That would explain why the free fraction is never mention in the paper.
Thanks for the explanation, that's really helpful. It's been quite a long time since I've done diff eq, I'm sure a lot has leaked out of my brain by now.
#!/usr/bin/env python
# coding: utf-8
# In[118]:
import numpy as np
import pandas as pd
import statsmodels.api as sm
import plotly.express as px
import plotly.graph_objects as go
# In[180]:
base_age = np.random.normal(loc = 50, scale = 15, size = 20)
age = np.concatenate([base_age, base_age]) + np.random.normal(0, 0.5, 40)
mecfs_status = np.concatenate([np.full(20, 0), np.full(20, 1)])
brain_metric = (0.2 * age) + mecfs_status + np.random.normal(loc=0, scale=0.1, size=40)
df = pd.DataFrame({
"Age": age,
"ME/CFS Status": mecfs_status,
"Brain Metric": brain_metric,
})
df.head()
# In[181]:
X = sm.add_constant(df['ME/CFS Status'])
y = df['Brain Metric']
model = sm.OLS(y, X)
results = model.fit()
fig = px.scatter(df, x='ME/CFS Status', y='Brain Metric', color="Age", opacity=0.65)
fig.update_traces(marker=dict(size=10))
fig.add_traces(go.Scatter(x=X['ME/CFS Status'], y=results.predict(X), showlegend=False))
fig.update_layout(
width=500,
height=500,
title={
'text': "Regression with only ME/CFS Status (Matched for age)",
'y':0.95,
'x':0.5,
'xanchor': 'center',
'yanchor': 'top'
}
)
fig.show()
print(results.summary())
# In[182]:
X = sm.add_constant(df[['ME/CFS Status', 'Age']])
y = df['Brain Metric']
results = sm.OLS(y, X).fit()
xrange = [X['ME/CFS Status'].min(), X['ME/CFS Status'].max()]
yrange = [X['Age'].min(), X['Age'].max()]
xx, yy = np.meshgrid(xrange, yrange)
pred = results.predict(sm.add_constant(np.c_[xx.ravel(), yy.ravel()]))
pred = pred.reshape(xx.shape)
# Generate the plot
fig = px.scatter_3d(df, x='ME/CFS Status', y='Age', z='Brain Metric', color="Age")
fig.update_traces(marker=dict(size=3))
fig.add_traces(go.Surface(
x=xrange,
y=yrange,
z=pred,
opacity=0.5,
colorscale=[[0, 'lightblue'], [1, 'lightblue']],
showscale=False,
))
fig.update_layout(
width=800,
height=600,
title={
'text': "Regression with ME/CFS Status and Age (Matched for age)",
'y':0.95,
'x':0.5,
'xanchor': 'center',
'yanchor': 'top'
})
fig.show()
print(results.summary())
# In[ ]:
# In[184]:
base_age = np.random.normal(loc=50, scale=15, size=20)
age = np.concatenate([base_age, base_age + 10]) + np.random.normal(0, 0.5, 40)
mecfs_status = np.concatenate([np.full(20, 0), np.full(20, 1)])
brain_metric = (0.2 * age) + mecfs_status + np.random.normal(loc=0, scale=0.1, size=40)
df = pd.DataFrame({
"Age": age,
"ME/CFS Status": mecfs_status,
"Brain Metric": brain_metric,
})
df.head()
# In[185]:
X = sm.add_constant(df['ME/CFS Status'])
y = df['Brain Metric']
model = sm.OLS(y, X)
results = model.fit()
fig = px.scatter(df, x='ME/CFS Status', y='Brain Metric', color="Age", opacity=0.65)
fig.update_traces(marker=dict(size=10))
fig.add_traces(go.Scatter(x=X['ME/CFS Status'], y=results.predict(X), showlegend=False))
fig.update_layout(
width=500,
height=500,
title={
'text': "Regression with only ME/CFS Status (Unmatched ages)",
'y':0.95,
'x':0.5,
'xanchor': 'center',
'yanchor': 'top'
}
)
fig.show()
print(results.summary())
# In[186]:
X = sm.add_constant(df[['ME/CFS Status', 'Age']])
y = df['Brain Metric']
results = sm.OLS(y, X).fit()
xrange = [X['ME/CFS Status'].min(), X['ME/CFS Status'].max()]
yrange = [X['Age'].min(), X['Age'].max()]
xx, yy = np.meshgrid(xrange, yrange)
pred = results.predict(sm.add_constant(np.c_[xx.ravel(), yy.ravel()]))
pred = pred.reshape(xx.shape)
# Generate the plot
fig = px.scatter_3d(df, x='ME/CFS Status', y='Age', z='Brain Metric', color="Age")
fig.update_traces(marker=dict(size=3))
fig.add_traces(go.Surface(
x=xrange,
y=yrange,
z=pred,
opacity=0.5,
colorscale=[[0, 'lightblue'], [1, 'lightblue']],
showscale=False,
))
fig.update_layout(
width=600,
height=600,
title={
'text': "Regression with ME/CFS Status and Age (Unmatched ages)",
'y':0.95,
'x':0.5,
'xanchor': 'center',
'yanchor': 'top'
})
fig.show()
print(results.summary())
Yes, that is what I think is going on, though they don't go into detail so I'm not certain. I assume this is somewhere in earlier papers and I just haven't found it yet.
Sorry, "ignoring" was the wrong word. I just meant that for some reason they aren't calculating/reporting a value ("NII-Free") that corresponds to those larger values of D in the same way "NII-RF" corresponds to small D (other papers using the same methods/equation do report a free value). You're right (or at least, it would be my guess too) that they still need to take the free fraction into account, in the denominator, to report all these values as fractions of the total.
I don't think it's circular. When we give age to the model, it can predict how much the brain metric would change due to age if ME/CFS status was held steady. For example, you can look at the 2nd plot above (the 1st 3d plot) and imagine the model is predicting a line for age but only in controls (ME/CFS status = 0). It's not unreasonable to think it can fit a nice slope for age. It just does it for the whole sample at once to get one slope for everyone.
If the sample is restricted to a small age range, then it does decrease variance. And it also reduces the possibility of non-linear effects at extreme ages. So using a restricted age range increases the likelihood of detecting a true effect. But if a study fits a model where the age range is very wide, and still gets a significant result, I don't think it's inherently an issue.
I'm not sure why what I posted would make you more suspicious of controlling for confounders.
What I mean by circular is that the effect of age is calculated from the sample. If by chance something weird is going on in our sample that skews the relationship between age and the signals for some individuals, that might result in us making an adjustment that doesn't reflect what is true in the wider population.
I'm not entirely sure what you mean. Yes, various things can also be affecting the brain metric apart from the variables in the model, leading to additional noise and confounding, but this is an issue whether age is added as another covariate with ME/CFS status or not. If we add age, we can at least then estimate what the slope would be if age were held constant. The resulting slope for ME/CFS status may still be confounded by other things, but at least we can be more assured that the slope isn't due to comparing 20 year olds to 40 year olds.
I wouldn't describe it as "falsely skewing the data" to control for HADS. We can interpret the result as the effect of ME/CFS status on the brain metric if the HADS score is held constant. In other words, if we have a healthy person and a person with ME/CFS that have identical HADS, what would be the difference in the brain metric. I'd expect it to show a smaller effect of ME/CFS on the brain metric, since I think HADS would somewhat be a proxy for ME/CFS severity. So it may tend to somewhat obscure a true ME/CFS effect.
I mean that the estimate of what the slope would be if age were held constant could be wrong, the assessed impact of age on the signals could be wrong, as in not reflective of a true population effect.
Mm, I don't think the topic is intuitive enough for me to be able to respond in a way that actually helps, so I'll probably just leave it there. You may be describing a real issue, but I don't have the capacity to think about exactly what you're talking about right now.
It wouldn’t be adding any problems that weren’t already there in your participant selection. What adding age as a covariate allows you to do is:
I think this would show as less fibre fraction (NII-FF) while this measure was increased in ME/CFS.